=p(i,t)(Xi,t;yobs,i,t)d=1D dt qd(i,t;dt)/n=1Np(n,t)(Xn,t;yobs,i,t)d=1D dt qd(n,t;dt).

The updating mechanisms are therefore obtained by using () and () with the new weights (REF ). The work in
[1]} showed that convergence of MPMC as \(N\)  increases can be established using the same approach as in [2]}, [3]}. The argument also applies for the augmented densities on \(\Theta \times \mathcal {X}\)  in this likelihood-free setting.
